
where the first inequality follows from (REF ) and (REF ), and
the last inequality follows from (). Let
\(\delta =\epsilon +\delta _1+\delta _2\) . By the chain rule of the mutual
information [1]},
\(n(R_1-\delta ) &\le I(W_1;Y_1^{n}|W_2)-I(W_1;Y_2^{n}|W_2)\\& = \sum _{i=1}^{n}\left[ I(W_1;Y_{1,i}|W_2,Y_{1,i+1}^{n})-I(W_1;Y_{2,i}|W_2,Y_2^{i-1})\right] \\& = \sum _{i=1}^{n}\left[ I(W_1;Y_{1,i}|W_2,Y_{1,i+1}^{n},Y_2^{i-1})-I(W_1;Y_{2,i}|W_2,Y_{1,i+1}^{n},Y_2^{i-1})\right] \) 
